The office of any trustee or director of any institution receiving state aid, appointed by the Governor or the General Assembly, who, for a period of two successive years, has failed to attend any of the meetings of the board of trustees or directors of which he is a member, shall be vacant, provided such trustee or director shall have had notice of each of such meetings; and, unless otherwise provided by statute, regulation or bylaw governing such board of trustees or directors, such board shall fill such vacancy.